Slide rule



Feb. 1o, 1925.

c. s.AL.ARKEY SLIDE RULE Filed Jan. 21, 1924 INVENTOR ATTORN EY Patented Feb. 10, 1925. .Y

UNITED STATES 1,525,752 PATENT OFFICE.

CHARLES S. LABKEY, 0F TULSA, KLAHOIA.

SLIDE RULE.

Application tiled January 21, 1924. Serial No. 687,839.

To all whom #may coment:

` Be it known that I, CHARLES S. Lanxm', a citizen of the United States, residing at Tulsa, in the county osTulsa and State of Oklahoma, have invented a new and useful Slide Rule, of which the following is a speciication.

My invention relates to improvements in slide rules in which the scales are subdivided into equal parts and arranged in a series across the length of eachv face of the rule; and the objects of v:my improvements are, first, to provide scales which can be read t0 a `greater number of significant figures than can be read on rules of the same length now in use; second, to arrange and designate such scales so that a ready reference may be had from one to another.

I attain these objects by the arrangement illustrated in the accompanying drawing, in which- Figure 1 represents one face and Figure 2 the opposite or reverse face of the rule.

Similar numerals refer to similar parts in each view.

The slide 1 is arranged to move along the sides or body 2 3, which parts 2 3 are connected together by some suitable mechanical arrangement not shown in the drawing so that they function as one rigid part.

In Figure 1 on the slide 1 are shown four scales designated respectively C1, C2, C, and. C4, which scales taken together in sequence as shown represent one continuous logarithmic scale or cycle, corresponding in its nature to the C-scale of the ordina Mannheim slide rule, each one of which four scales vbeing equal in length to one-fourth of the complete logarithmic cycle. 0n the side 2 the D1 and D, scales are exactly similar to and correspond with the C, and C2 scales of the slide 1; likewise, on the side 3 the l)3 and D4 scales are exactly similar to and correspond with the C3 and C,t scales of the slide'l.

In Figure 2, on the slide 1, are shown Jfour scales designated respectively B1', B11, BI2 and B2, the B1 and B2 scales constituting one complete logarithmic scale or cycle divided into two parts of equal length, and the BI1 and BI2 scales also constituting one complete logarithmic scale or cycle divided into two parts of equal length, but arranged in a reverse yorder so that the numbers represented thereon are reciprocal to the numbers shown on the B1 and Bz scales. On

the sideB, scale A1 corresponds with and is exactly similar to scale B1 of the slide 1; and likewise on side 2 scale A, corresponds with and is exactly similar to-scale B2 of the slide l. On the side 3 is shown an evenly graduated scale Lm, which is designed to give the mantissas of lo arithms of numbers shown on the D, and di scales of Figure 1; likewise, on side 2 is shown a similar scale LH, which is designed to give the mantissas of logarithms of numbers shown on the D3 and D4 scales of Fi re 1.

The numbers and letters of scales IBI,L and .BI2 are to be of a contrasting color to the numbers and letters of other scales for convenience of reference.

The order of graduating or subdividin the scales shown in each view is indicat where each change occurs by the complete graduations being shown, it being intended that such order be followed in graduating each scale to the point where a dilerent order is indicated.

It will be noted that subscript numbers are used to designate parts of each complete scale; thus A2 designates the second part of the A scale, and C,1 designates the fourth part of the C scale, etc. The use of subscripts in this manner facilitates operations performed on this rule, by furnishing ready reference from one scale to' another, While at` the same time retaining the ident-ity of each scale in its entirety.

In multiplication or division, simple operations of addition or subtraction respectively of subscripts determine the subscript of the scale on which the result the operation may be read. In finding the squares or square roots of numbers, reference is made from the odd numbered subscripts of one scale to the odd numbered subscripts of another, or from the even numbered subscripts of one scale to the even numbered subscripts of another.

These and further uses are explained in detail by the following examples:

In multiplication, when the slide is moved to the right, readings fromI the C to the I) scales are to be found on the D scale having a subscript equal to either 1 or 5 less than the sum of the subscripts of the scales on which the two numbers to be multiplied are found, 1 being subtracted when the sum is 5 or less and 5 being subtracted when the sum is 6 or more. When the slide is moved to the left, the same rule applies except that 0 or 4 .is subtracted instead of 1 or 5, 0 being subtracted when the sum is 4 or less and 4 being subtracted when the sum is 5 or more.

For example, in multiplying 23 by 12,

the slide must be moved to the right. 23 is found on thc D2 scale and 12 on the C1 scale. The sum of subscripts is 3. Deducting 1 (the sum being less than 5), the product should be found on the D2 scale. Thus moving the slide to the right and setting the'left hand index of the C scale to 23 on the D2 scale, 276 is read on the D2 scale op osite 12 on the C1 scale.

YCr, on multiplying 87 by 55, the slide must be moved to the left. 87 is found on the D4 scale and 55 on the C'scale. The sum of subscripts is 7. Deducting 4 (the sinn being greater than 5), the product should be found on the D3 scale. Thus moving -the slide to the left and setting the right hand index of the C scale to 87on the D4 scale, 4785 is read on the D3 scale opposite 55 on the C3 scale.

In division, when readings are made with the slide moved to the right, either 1 or 5 is added to the subscript of the D scale on which the dividend is found, from which the value the subscript of the C scale on which the divisor is found is subtracted to obtain the subscript of the D scale on which the quotient is read; 1 being added if the subscript of the C scale is equal to or less than the subscript of the D scale, and 5 being added if the subscript of the C scale is greater than that of the. D scale.v When readings are made with the slide moved to the left, the same rule applies except that either 0 or 4 is added to the subscript of the D scale instead of l or 5, 0 being added when the subscript of the. C scale is less than that of the D scale, and 4 being added when the subscript of the C scale is equal to or greater than that of the D scale.

For example, in dividing 288 by 12, the slide is moved to the right until the divisor 12 on the C, scale is opposite the dividend 288 on the D2 scale. The quotient l24 is then read on the D2 scale opposite the left hand index of the C scale, since by the rule of subscripts, 1 must be added before the difference is taken,'giving 2 for the subscript of the D scale on which to find the quotient.

Or, in dividing 750 by 15, the slide is moved to the left until the divisor 15 on the Cl scale is opposite the dividend 750 on the D, scale. The quotient 50 is then read on the D3 scale opposite the right hand index of the C scale, since by the rule of subscripts O must be added before the difference is taken, giving 3 for the subscript of the D scale on which to find the quotient.

In examples involving the squares of numbers, reference is madefrom the C scale to the B scale or from the D scale to the lA scale, as with the ordinary Mannheim rule, the subscripts used to designate parts of these scales facilitating such reference. Thus the squares of numbers shown ,on the D1 and D3 scales are to be found circle of radius 5, by the formula A=1cR2,' l

5 is found on the D3 scale. Its square 25 is then found by direct reference on the A1 scale, to which either index of the B scale may be set and the area. 78.54 be read on the A2 scale, opposite a on the B,L scale if the` slide is moved to the left, or on the B2 scale if the slide vis moved to the right. In this example reference was made from an odd numbered subscript of the'D scale to the odd'nuinbered subscript of the A scale.

In examples involving -the square roots of numbers, this process is reversed, the square roots of numbers shown on the A1 scale being read on the D1 and D3 scales and the square roots of numbers shown on the A2 scale being read on the D2 and D4 scales. The same relation also exists between the B and C scales. If the number of two digits each, beginning at the decimal point, the first period will contain either one or two digits. When it contains one digit, reference is from the A1 scale to the Dl'scaleor from the A2 to the D2 scale, depending upon which of the A scales the number is found; if it contains two digits, reference is from the A1 to the D3 scale or from the A2 to the D2 scale, depending upon which of the A scales the number is found; likewise with the B and C scales.

For example, in finding the square root 'of 25, since this number contains two digits, reference is from the A1 scale, where the 25 is found, to the D3 scale, where the root `5 is read exactly opposite the 25; while for the square root of 250, since the first period of this number contains one digit, reference is from the A1 scale to the D1 scale, where the root 15.81 is read exactly opposite the 250.

The subscripts used with the L scale are for reference from the D scale, when logarithms of numbers shown on the D scale are desired, or` vice versa; thus the logarithms of numbers on the D1 scale are to be found on the L1 scale, those on the D2 scale on the L2 scale, et cetera. Since the L scale is an evenly divided scale, it is not necessary to repeat parts of this scale, hence the L1 and L2 scales are shown as one with a double set Aof scale numbers; likewise, the

Ll and L, scales, the lesser set of scale numbers being read for the lesser subscript number and the eater set of scale numbers being read or the greater subscript number, in each instance.

Other slide rules have been made where scales are divided into parts or segments, but inorder to know upon what segment of ascale to read the result of a calculation, it is necessary to resort to some table or mechanical device, while by Athis rule the desired segment is directly indicated by the subscript numbers used to designate each separate part or segment of a complete scale, as shown by the foregoing examples.

Parts or segments of scales on other slide rules have also been designated by numbers in addition to the letters used, but such designation has been for the purpose of identifying such. parts or segments, only. On this rule, numbers used in the subscript form are for the purpose of direct reference between different scales.

(lo-logarithmicv scales or cycles have been used in registry with logarithmic scales or cycles, from which reciprocals of numbers may be read from the one scale to the other, but the principle has never been applied to a scale divided into parts or segments, such as is shown on my rule in the comparison of the BIl and BI2 scales with the B, and B2 scales.

' I claim:

1. In a slide rule having two fixed bars and one slidin bar, a logarithmic scale or cycle divide into four equal parts or segments, two of which se ments on one of the said fixed bars and t e other two of which segments on the other of the said fixed bars, with a logarithmic scale or cycle divided into two equal parts or segments on the sa'id sliding bar, so arranged that the s uares of numbers on the fixed bars may e read directly on the sliding bar from the one scale to the other.

2. In a slide rule having two fixed bars and one sliding bar, a logarithmic scale or cycle divided into two equal parts or segments, one of which segments on one of the said fixed bars and the other of which segments onthe other of the said fixed bars, with a logarithmic'scale or cycle divided into four equal parts or segments on vthe said sliding bar, so arranged that the squares of numbers on the sliding bar may be read directly on the fixedbar from the lone scale to the other.

3. In a slide rule having two fixed bars and one sliding bar, a logarithmic scale or cycle divided into two equal parts or seg# ments, with a co-logarithmic scale or cycle divided into two equal parts or segments in -fixed registry therewith, such that the resuch that in comparing segments of scales for multiplication or division, the sum of subscripts of the scale segments compared will indicate the scale segment on which the result of multiplication may be read and the difference of subscripts of the scale segments compared will indicate the scale segmeit on which the result of division may be rea 5. In a slide rule having two fixed bars and one sliding bar, a logarithmic scale or cycle divided into four equal parte or segments, two of which segments on one of the said fixed bars, and the other two of which segments on the other of the said fixed bars, with a co-logarithmic scale or cycle divided into two equal parts or segments on the said sliding bar, so arranged that the squares of the reciprocals of numbers on the fixed bars may be read directly on the sliding bar when brought into registry therewith from the one scale to the other.

6. In a slide rule having two fixed bars and one sliding bar, a logarithmic scale or cycle divided into four equal arts or segments, with an evenly graduated scale which may be brought into registry therewith, such that the mantissas of logarithms of numbers may be read directly from the logarithmic scale to the evenly graduated scale.

7 In a slide rule having two fixed bars and one slidingbar, an evenly graduated arithmetic scale divided into equa arts or segments, such that portions of t e scale may be repeated over the same graduations by the use of multiple sets of scale numbers, and such that each set of scale numbers -represents mantissas of logarithms of numbers on a logarithmic scale or cycle divided into the same number of equal arts-or segments and brought into registry t erewith.

'CHAS. S. LARKEY. 

